# Andris Alberts BuikisUniversity of Latvia | LU · Institute of Mathematics and Computer Science

Andris Alberts Buikis

Dr. habil. math.

## About

478

Publications

17,242

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706

Citations

Citations since 2016

Introduction

Additional affiliations

May 2006 - present

Education

September 1957 - November 1963

## Publications

Publications (478)

In this paper we develop mathematical model for three dimensional heat equation for the system with hollow wall and fin and construct its analytical solution for two hollow cylindrical sample. The method of solution is based on Green function method for one hollow cylinder. On the conjugation conditions between both hollow cylinders we construct so...

The paper is destined for use in medicine, psychology, in man’s self-development training, breathing technique’s training, in the field of stress resistance, health promotion, strengthening of the capacity for work; and it relates to the apparatus and methods for detection of the heart rate variability and it’s may be used in providing biofeedback...

In this paper we develop mathematical models for 3-D hyperbolic heat equation. This equation describes the mathematical models for steel quenching in highly agitated water and wave power of energy by waves of ocean surface. 1-D model is obtained from 3-D problem by conservative averaging method. We construct their exact analytical solutions by the...

In this paper we look over history of conservative averaging method in last 100 years. Some well known mathematicians in classical papers investigated problems with non-classical boundary conditions, which have derivatives in boundary conditions equal or higher as derivatives in the main partial differential equation. Forty or fifty years ago it wa...

Of the manufacturing the insulated technical fabric from glass fibre.

The work shows the perturbation of the Buckley- Leverett function to exert strong influence on the solution

The paper is established for use in medicine, psychology, in man's self-development training, breathing technique's training, in the field of stress resistance, health promotion, strengthening of the capacity of work. We involve new technology for registration of time interval between two consecutive EKG RR intervals (R peaks): a) The time between...

In this paper we develop mathematical models for 3-D, 2-D and one-dimensional hyperbolic heat equations (wave equation or telegraph equation) with inner source power and construct their analytical solutions for the determination of the initial heat flux for cylindrical sample. In some cases we give expression of wave energy. Some solutions of time...

The paper is destined for use in medicine, psychology, in man’s self-development training, breathing technique’s training, in the field of stress resistance, health promotion, strengthening of the capacity for work. We involve new technology for registration of time interval between two consecutive EKG RR intervals (R peaks) or pulse wave peaks, wh...

The paper is destined for use in medicine, psychology, in man’s self-development training; breathing technique’s training, in the field of stress resistance, health promotion, strengthening of the capacity for work. We involve new technology for registration of time interval between two consecutive EKG RR intervals (R peaks) or pulse wave peaks, wh...

The paper is destined for use in medicine, psychology, in man's self-development training, breathing technique's training, in the field of stress resistance, health promotion, strengthening of the capacity for work. We involve new technology for registration of time interval between two consecutive EKG RR intervals (R peaks) or pulse wave peaks, wh...

In this paper we develop mathematical models for three an two dimensional stationary hyperbolic heat equations with inner source power and we construct their analytical solutions. We solved three-dimensional problem for two contacted rectangles with inner heat sources and full non-homogeneous boundary conditions. The application for such mathematic...

The future of the energy (in Latvian)

In this paper we develop mathematical models for 3-D, 2-D and one-dimensional hyperbolic heat equations (wave equation or telegraph equation) and construct their analytical solutions for the determination of the initial heat flux for rectangular samples. In some cases we give expression of wave energy. Some solutions of time inverse problems are ob...

In this paper we develop mathematical models for 3-D, 2-D and one-dimensional hyperbolic heat equations (wave equation or telegraph equation) and construct their analytical solutions for the determination of the initial heat flux for rectangular samples. In some cases we give expression of wave energy. Some solutions of time inverse problems are ob...

Green’s function method for connected regular domains and applications of the conservative averaging method for transient processes

In this paper we study the problem of the diffusion of one substance through the pores of a porous multi layered material which may absorb and immobilize some of the diffusing substances with the evolution or absorption of heat. As an example we consider circular cross section wood-block with two layers in the radial direction. We consider the tran...

In this paper we look over history of conservative averaging method in last 50-100 years. Some well-known mathematicians in classical papers investigated problems with non-classical boundary conditions, which have derivatives in boundary conditions equal or higher as derivatives in the main partial differential equation. Forty or fifty years ago it...

In this paper we develop mathematical models for three dimensional hyperbolic heat equations (wave equation or telegraph equation) with inner source power and construct their analytical solutions for the determination of the initial heat flux for cylindrical sample. As additional conditions the temperature and heat flux at the end time are given. I...

We consider averaging methods for solving the 3-D boundary-value problem of second order in multilayer domain.
The special hyperbolic and exponential type splines, with middle integral values of piece-wise smooth function interpolation are considered. With the help of these splines the problems of mathematical physics in 3-D with piece-wise coeffic...

In this paper we develop mathematical models for 3-D, 2-D and 1-D hyperbolic heat equation and construct their approximated analytical solutions by the method of conservative averaging for the determination of the initial heat flux for one domain. Important is that in this paper we propose non-polynomial form of approximation function. Approximate...

In this paper we develop mathematical models for 2-D and 1-D hyperbolic heat equations (wave equation or telegraph equation) and construct their exact analytical solutions for the determination of the initial heat flux for rectangular samples. Some solutions of time inverse problems are obtained by Green function method as time inverse problems. Ap...

In this paper we consider averaging methods for the solution of the 3-D initial boundary problem of second order with piece-wise parameters in multi-layer domain. The special hyperbolic and exponential type splines with averaged integral values of piece-wise smooth function's interpolation are considered. With the help of these splines the problems...

Latvian mathematical Yearbook. No. 7, 1970.

Latvian mathematical Yearbook. No. 7, 1970.

Latvian mathematical Yearbook, No. 7. Riga, 1970.

Development of Latvia until 2010 context on province and Europe.
(In Latvian)

Profession 0647 – “Applied Mathematics.” Publishing house of Moscow university, 1980.

Collection "Application of modification polymers materials in the drainage system constructions." Jelgava, 1983.

Collection "Application of modification polymers materials in the drainage system constructions." Jelgava, 1983.

Abstracts of VII All-union Conference “Qualitative Theory of Differential Equations.” Jurmala, April 3-9, 1989. In Russian language.

Abstracts of republic Conference “Theory and numerical methods for the solution differential equation with boundary condition.” Jurmala, December 20-21, 1988. Latvian university, Riga, 1988. (In Russian language)

Scientific – technical collection on oil output. All-union oil-gas scientism and investigation institute. Moscow, Nedra, 1970. In Russian language

Proceedings of higher educational institution “Applied problem of mathematical physics.” Latvian university, Riga, 1988.

Collection “Investigation of applied mathematics”, Issue 9. Kazan university, 1981. In Russian language.

Collection “Applied Problems Theoretical and Mathematical Physics.” Latvian university, Riga, 1977.

Theoretical and Applied Problems Numerical Mathematics and Mathematical Physics. Latvian university, 1985.

Republic Conference “Engine methods of the solving filtration theory.” Kazan, 1989. In Russian language.

Profession 0647 – “Applied Mathematics.” Publishing house of Moscow university, 1978.

Abstracts of All-union young scientists Conference “Numerical Methods and Mathematical Modelling.” Minsk, 1984.

All-union Conference ”Functional Methods in the Applied Mathematics and Mathematical Physics.” Tashkent, 1988, Part II.

European Commission, PECO 1993. Project summaries. Catalogue of participation in the Third Framework Programme in 1993. January 1996.

11th ECMI Conference, Torre Normanna, Altavilla Milicia, Palermo- Italia, 26-30 September,2000.

20th International Conference on Mathematical Modelling and Analysis. May 26-29, 2015, Sigulda, Latvia

Physical-Chemical Methods to Raise Oil Output. Moscow, 1985. In Russian language

Proceeding "Mathematical Models, Analytical and Numerical Methods on the Transfer Theory", Minsk, 1986. (In Russian language)

Numerical Methods for the Continuous Medium. No. 4, vol. 16, 1985. In Russian language

Applied problems theoretical and mathematical physics. Latvian university. Riga, 1978.

The doctor of the physic - mathematical sciences. Kazan, 1987

Numerical methods of the solutions problems of the filtration of the incompressible multiphase fluid. Novosibirsk, 1987. (In Russian language).

Latvian Mathematical Yearbook, No. 32, 1988. (In Russian language)

Preprint No. 144 of Institute of Physics Latvian Academy of Sciences. Salaspils, 1989.

Konferences "Līdzsvarota attīstība- Latvijas attīstībai" tēzes. Rīga, 1994. gada 19.-20. marts.

Latvian university. Seminar "Mathematical Modelling and Parameter Identification of Transfer Processes in Non homogeneous Media". Riga, 1992

Dynamics of multiphase medium (IN Russian language). Novosibirsk, 1985.Proceedings of All-union seminar "Contemporary problems and mathematical methods in the theory of filtration".

Abstracts of the All-union school-seminar young scientists and specialists. Svetligorsk, September 19-24, 1988. (In Russian language)

Latvian Mathematical Yearbook, No. 25, 1981.

Latvian Mathematical Yearbook, No. 23, 1979.

Latvian Mathematical Yearbook, No. 26, 1982.

Latvian university, 1994. "The mathematical simulation. Applied problems of mathematical physics."

Abstracts of Fifth European Conference on Numerical Mathematics and Advanced Applications. Prague, Czech Republic, August 18-22, 2003.

Third Conference on Numerical methods and approximation theory. Niš, Yugoslavia, August 18-21, 1987

4th IASME / WSEAS International Conference on HEAT TRANSFER, THERMAL ENGINEERING and ENVIRONMENT. Elounda, Agious Nikolaos, Crete Island, Greece, August 21-23, 2006.

Latvian university. "Mathematical Modeling. Applied Problems Mathematical Physics." Issue 2, 1991.

Journal "Electronic Modelling", No. 198. 1986, vol. 8, No. 6. Kiev, "Naukova Dumka"

8th Latvian Mathematical Conference. Valmiera, April 9-10, 2010.

Summary of candidate of sciences in the mathematics; specialty - numerical methods. Riga, 1970.

ECMI 94, 8th Conference of the European Consortium for Mathematics in Industry. University of Kaiserslautern, Germany, September 6-10, 1994.

Latvian Journal of Physics and Technical Sciences. No. 3, 1996.

ICM, Warszawa, 1992. Short Communications (Abstracts), XII. Section 15: Numerical methods. Section 18: New applications of mathematics.

Banach Center Publications, vol. 24. "Numerical analysis and Mathematical modelling." Warsaw, 1990.

Institute of Mathematics of Latvian Academy of Sciences and the university. "The mathematical simulation. Applied tasks of mathematical physics." 1994.

Latvian Journal of physics and technical Sciences. No. 5, 1995.

Riga, Latvia, 2002. Research "Mathematical Models for Industry". P.76-78.

Latvian Journal of Physics and Technical Sciences, No.4, 2002.

Abstracts of 12th Conference of the European Consortium for Mathematics in Industry. Jurmala, Latvia, September 10-14, 2002.

Abstracts of the 13th International Conference on Mathematical Modelling and Analysis, June 4- June 7, 2008.

## Projects

Projects (2)

I'm working on 1) Heart rate variability; 2) Green function method for non-canonical domain with application to PC ventilation; 3) method of conservative averaging in the last 100 years.